We recently described rapid quantitative pharmacodynamic imaging, a novel method for estimating sensitivity of a biological system to a drug. Measuring the sensitivity of an organ to a drug in vivo is a common, important research goal. Here we revisit the simulation testing using a Bayesian method to provide continuous estimates of the PKPD parameters.

Figure 2 provides an example result from one time course, to orient the reader to the following summary.

This simulation used a simple noise model that may be best suited to a temporally stable, quantitative outcome measure, such as positron emission tomography, arterial spin labeling, or quantitative BOLD.

Even with the relatively simple signal and noise models adopted for this initial testing, the tested method appeared to handle reasonably the in vivo data from a BOLD phMRI study (Figure 7). The QuanDyn™ method described here has several potential advantages compared to the traditional approach to quantifying a drug effect, which is to estimate the population EC50 by sampling a wide range of doses, one dose per subject and several subjects per dose. The following information was supplied regarding the deposition of related data: The simulated data sets (1000 time courses for each set of parameter values and noise level) are available at the journal web site as Supplementary Data. JK performed the experiments, analyzed the data, contributed analysis tools, reviewed and critiqued the manuscript.

The other authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Some of these results were presented previously (JK, GB, KB: A novel analysis method for pharmacodynamic imaging.

The aim of this study is to rank some features that characterize the psychological dynamics of cooperative team work in order to determine priorities for interventions and formation: leading positive feedback, cooperative manager and collaborative manager features. Even though the assumption of conditional independence is violated on numerous occasions in real applications, NB still performs well in many situations [41].

The 12U Chatsworth Heat Travel Baseball Team is on the path for the trip of a lifetime to Cooperstown Dreams Park in June 2014. This means that you will not need to remember your user name and password in the future and you will be able to login with the account you choose to sync, with the click of a button. This page doesn't support Internet Explorer 6, 7 and 8.Please upgrade your browser or activate Google Chrome Frame to improve your experience. We tested its accuracy in simulated biological signals with varying receptor sensitivity and varying levels of random noise, and presented initial proof-of-concept data from functional MRI (fMRI) studies in primate brain. The traditional approach is to independently measure biological responses to a range of different doses of drug.

The Bayesian approach also identifies data too noisy to produce meaningful parameter estimates (using a model selection package described below). The Toolbox computes the posterior probability for the set of models (Bretthorst, 1988) given a 4d data set. Therefore, we computed a signal-to-noise ratio (SNR) to simplify comparisons across the various input values of EC50 and noise. These studies were approved by the Washington University Animal Studies Committee (protocols # 20020085, 20050126).

Prior probabilities for all other parameters were the same as described above for the simulated data. Note that the parameter estimates are (approximately) the best estimates for the provided noisy data, even though they differ slightly from the input values used to produce the data. Figure 5 shows the mean estimated EC50 as a function of the input EC50; as expected, accuracy is best with higher SNR.

Time-signal curves from in vivo data from a phMRI study, in red, with the selected model in dark blue. The Bayesian Data-Analysis Toolbox successfully avoided false positives, correctly refraining from identifying a signal in every noise-only time course, even where sensitivity was 100%.

However, because the PKPD model E(C) is simply added to the baseline model B(t), the latter can be replaced with a more complex signal, if needed, for non-quantitative imaging methods. However, prior to initiating an expensive imaging study, one would determine the appropriate family of PKPD models for the drug to be tested, based on traditional dose-response experiments. Further validation will require a larger set of similar multi-dose phMRI data, and comparison data from a more traditional dose-response study design.

From a dataset of 20 cooperative sport teams (403 soccer players), the characteristics of the prototypical sports teams are studied using an average Bayesian network (BN) and two special types of BNs, the Bayesian classifiers: naive Bayes (NB) and tree augmented naive Bayes (TAN). IntroductionIn high performance sports, it is crucial to rank features to determine their degree of influence in a cooperative work team, with the ultimate objective of maximizing the team’s performance. From dreaming of making the major leagues to weekend players, baseball draws fans from all walks of life. However, the initial simulation testing used a simple iterative approach to estimate pharmacokinetic-pharmacodynamic (PKPD) parameters, an approach that was computationally efficient but returned parameters only from a small, discrete set of values chosen a priori. Bayesian methods have been used successfully in other PKPD analyses (Lavielle, 2014, to cite but one example). A Markov chain (Gilks et al., 1996) is used to draw samples from the joint posterior probability for all of the parameters including the choice of model.

Each animal was studied twice, at least 2 weeks apart, producing 8 regional time-signal curves. SNR for each estimate is shown by the width of the marker, as indicated by the legend at lower right. In time courses with a signal, mean accuracy was reasonable even in the face of low SNR, as shown in Figures 5, 6. For instance, Fourier series have been used to model typical BOLD-sensitive fMRI data over long time intervals. One might adapt the traditional approach by repeatedly scanning a single subject, one dose per scan session, but that option brings its own complications, including scientific concerns such as sensitization or development of tolerance with repeated doses in addition to the practical and ethical consequences of repeated scanning sessions in each subject.

KB is an Associate Editor for the Brain Imaging Methods section of Frontiers in Neuroscience. BNs are selected as they are able to produce probability estimates rather than predictions. Along these lines, several studies have been carried out in the field of social psychology, where features, such as motivation, cohesion, leading positive feedback or social attraction, play an important role due to their close relation to performance [1,2,3,4,5].Cooperative team work is a fact well known today [6], even when taking into account the associated psychological factors’ [7] analysis. Here we revisit the simulation testing using a Bayesian method to estimate the PKPD parameters. For the present purpose we applied a Bayesian data analysis package specifically designed for efficient voxelwise analysis of 4-dimensional imaging data (Bretthorst, 2014; Bretthorst and Marutyan, 2014). Furthermore, the errors were conservative, with EC50 usually erring on the high side (Figure 6). The baseline model B(t) could be optimized further to best suit a specific scanner, tracer or sequence, or to other experimental design choices. That option, like the population method, would also require that subjects receive doses substantially higher than the EC50, which may often be inappropriate in early human studies. KB conceived and designed the experiments, performed the experiments, analyzed the data, wrote the paper.

The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

BN results show that the antecessors (the “top” features ranked) are the team members’ expectations and their attraction to the social aspects of the task. However, it is difficult to find studies that relate the equipment they need to cooperate with effective performance [8]. This improved accuracy compared to our previous method, and noise without intentional signal was never interpreted as signal.

The initial simulation testing used a simple iterative approach to estimate pharmacokinetic-pharmacodynamic (PKPD) parameters including EC50, the plasma concentration of drug that produces half the maximum possible effect Emax.

Said differently, the most likely quantitative error was to report slightly lower sensitivity to drug, especially when sensitivity is in fact low. The choice of imaging method also affects the signal characteristics; for instance, typical BOLD implementations may not provide adequately linear responses to biological signal. The main node is formed by the cooperative behaviors, the consequences ranked at the BN bottom (ratified by the TAN trees and the instantiations made), the roles assigned to the members and their survival inside the same team.

Some psychological factors of collaborative teams have been studied more than others in terms of performance, such as cohesion [9,10] or group facilitators and blockers’ roles [11]. The iterative approach was computationally efficient but could only select EC50 from a short list of parameter values chosen a priori. Monte Carlo integration is then used to obtain samples from the posterior probability for each model and from the posterior probability for each parameter given the model. On the other hand, using a more traditional phMRI design, the magnitude of the acute BOLD response to a single dose of drug per imaging session did increase monotonically with larger doses (Miller et al., 2013). For all these reasons, the QuanDyn™ method may prove to be a better choice when single-subject responses are important, such as for medical diagnosis or individualized treatment dosing. Rapid quantitative pharmacodynamic imaging by a novel method: theory, simulation testing and proof of principle. These results should help managers to determine contents and priorities when they have to face team-building actions.

Features, such as the specificity of the jobs [12] (or playing positions, in this case), generating performance expectations, the motivational climate generated by the manager [13] and the leadership styles of the coach, which are not usually studied, are considered here in this paper.Bayesian networks (BNs) [14,15,16,17,18], well suited to reason with uncertain domain knowledge, can be applied to aid teams by providing cooperative and collaborative work characterization estimates. The success with the simulated data, and with the limited fMRI data, is a necessary first step toward further testing of rapid quantitative pharmacodynamic imaging.

For the present analysis we specified 2500 samples at each step (50 samples run in parallel, repeated 50 times).

We elsewhere discuss potential challenges related to moving this approach into humans (Black et al., 2013). BNs have been proven to be a strong tool to discover the relationships between variables that attempt to separate out indirect from direct association [8,19,20,21] and can capture the way an expert understands the relationships among all of the features [22]. Simulated annealing is used to minimize the risk of convergence to a non-global local maximum (see Bretthorst, 2014, appendix B, for details).

If the posterior probability for the model indicated the full model, B(t) + E(C(t)), was preferred, the package also returned values for EC50, ts, Emax, a0, a1, and a2.

Contrary to deterministic understanding of the causality phenomenon [23], BN modeling lies within the data mining and machine learning literature [24,25].

The software returns both the mean parameter values and the values from the simulation with maximum likelihood; the present report uses the latter. The network structure is a directed acyclic graph (DAG) where each node represents a random variable [26,27], and the arcs may represent causality [28,29,30]. BNs combine graph theory and probability theory to represent relationships between variables (nodes in the graph) [8,19].

They give a compact representation of a joint probability distribution via conditional independence.

BNs are the best known classifiers that are able to provide the probability distributions concisely and comprehensibly [31,32]. In [33], the authors considered BN model with the naive Bayes algorithm as one of the most effective classification algorithms.Recently, there has been increasing attention regarding the application of BNs in competitive sport contexts.

In the NB classifier, the class attribute is the single parent of each node of an NB network.

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